1. Johannes Kepler 1571-1630 Johannes Kepler was a German mathematician and astronomer who postulated that the Earth and planets travel about the sun in elliptical orbits. He gave three fundamental laws of planetary motion. He also did important work in optics and geometry. Through his career Kepler was a mathematics teacher at a Graz seminary school (later the University of Graz, Austria), an assistant to Tycho Brahe, court mathematician to Emperor Rudolf II, mathematics teacher in Linz, Austria, and court astrologer to General Wallenstein. He also did fundamental work in the field of optics and helped to legitimize the telescopic discoveries of his contemporary Galileo Galilei. He is sometimes referred to as "the first theoretical astrophysicist", although Carl Sagan also referred to him as the last scientific astrologer.

2. How did Kepler come up with the Three Laws of Planetary Motion? In the interplay between quantitative observation and theoretical construction that characterizes the development of modern science, we have seen that Brahe was the master of the first but was deficient in the second. The next great development in the history of astronomy was the theoretical intuition of Johannes Kepler (1571-1630), a German who went to Prague to become Brahe's assistant.Kepler and Brahe did not get along well. Brahe apparently mistrusted Kepler, fearing that his bright young assistant might eclipse him as the premiere astonomer of his day. He therefore let Kepler see only part of his voluminous data. He set Kepler the task of understanding the orbit of the planet Mars, which was particularly troublesome. It is believed that part of the motivation for giving the Mars problem to Kepler was that it was difficult, and Brahe hoped it would occupy Kepler while Brahe worked on his theory of the Solar System. In a supreme irony, it was precisely the Martian data that allowed Kepler to formulate the correct laws of planetary motion, thus eventually achieving a place in the development of astronomy far surpassing that of Brahe. Unlike Brahe, Kepler believed firmly in the Copernican system. In retrospect, the reason that the orbit of Mars was particularly difficult was that Copernicus had correctly placed the Sun at the center of the Solar System, but had erred in assuming the orbits of the planets to be circles. Thus, in the Copernican theory epicycles were still required to explain the details of planetary motion. It fell to Kepler to provide the final piece of the puzzle: after a long struggle, in which he tried mightily to avoid his eventual conclusion, Kepler was forced finally to the realization that the orbits of the planets were not the circles demanded by Aristotle and assumed implicitly by Copernicus, but were instead the "flattened circles" that geometers call ellipses The irony noted above lies in the realization that the difficulties with the Martian orbit derive precisely from the fact that the orbit of Mars was the most elliptical of the planets for which Brahe had extensive data. Thus Brahe had unwittingly given Kepler the very part of his data that would allow Kepler to eventually formulate the correct theory of the Solar System and thereby to banish Brahe's own theory!

3. Law of planetary motion is one of three empirical laws of planetary motion stated by Johannes Kepler. The three laws of planetary motion were used by Sir Isaac Newton, when formulating his universal law of gravitation. Newton showed that an object subject to the *gravitational force from the Sun can follow an elliptical orbit, as specified by Kepler's first law of planetary motion. But it can also follow a parabolic or *hyperbolic path, depending on the *energy of the object. Therefore, a *comet might enter the solar system and leave without returning. Kepler's three laws of planetary motion do not take into account the perturbing gravitational effects of the planets on each other. But even the motions of just three bodies under mutual attraction have only a few special-case *analytical solutions. Fortunately, the Sun dramatically outweighs the planets and their motions become a two-body problem where one body is fixed (unless extreme accuracy is sought).

4. What are the 3 laws of planetary motion?

5. Kepler’s First Law states… “The path of any object in an orbit follows the shape of an ellipse, with the orbited body at one of the foci.” So what does all that mean? An ellipse is shaped like a circle that someone has sat on. It’s squished in the middle and bulges out on the ends. Foci (the plural form of the word focus) are two points inside the ellipse. If you were to push stick pins into the foci and put a loop of string around them, you could draw an ellipse.

6. Remember that the object being orbited sits at one focus, and the other object follows the path of the ellipse The sketch of the Earth orbiting the Sun should look like this… This means that sometimes the Earth is closer to the Sun, and sometimes further away. This is not the reason for summer and winter! The season on Earth are created by Earth’s tilt on its axis.

7. Kepler’s Second Law states… “An imaginary line from the sun to the planet sweeps out equal areas in equal times.” Figure 3 If we were to look at the area the Earth sweeps out in a 15 day period, first when close to the sun (Figure 3) and then when far away (Figure 4 ), we would get diagrams that look like this. Figure 4

8. Third Law: where he relates the radius of an orbit to it’s period of orbit (the time it takes to complete one orbit) “The square of the period of orbit, divided by the cube of the radius of the orbit, is equal to a constant (Kepler’s Constant) for that one object being orbited.” The formula looks like this... T = period (in any unit) r = radius (in any unit) K = Kepler's Constant Kepler's Constant is only a constant if the object being orbited stays the same. So, anything orbiting the sun has the same Kepler's Constant, just like anything orbiting the Earth has the same Kepler's Constant. The Sun and Earth Kepler's Constants will be different from each other.